742. ILLUSTRATIVE EXAMPLE I. If a cube of lead whose

edge is 3 inches weighs 12 pounds, what is the weight of a cube of lead whose edge is 2 inches?

743. ILLUSTRATIVE EXAMPLE II. A pyramid 9 feet high contains 48 cubic feet. What is the height of a similar pyramid that contains 100 cubic feet?

WRITTEN WORK.

48: 10098: x3

9X9X9X100 = 11.49...

Ans. 11.49... feet.

48

744. Examples for the Slate.

51. If an egg 24 inches in circumference weighs 1 ounce, what would another of the same form and consistency weigh whose circumference is 6 inches?

52. An ox measuring 7 feet in girth weighs 1500 pounds; what is the weight of an ox measuring 9 feet in girth?

53. If a bushel measure is 18 inches in diameter and 8 inches deep, what must be the diameter and depth of a halfbushel measure similar in form?

54. Estimating the mean diameter of the earth at 7912 miles, and that of the moon at 2160 miles, how many bodies of the size of the moon could be made from the bulk of the earth? 55. If the bulk of Saturn be 1000 times as great as that of the earth, what is the diameter of Saturn?

56. At what distance from the top must a cone 12 inches high be cut parallel with the base, that the cone may be divided into two equivalent parts?

57. Mr. Root has three stacks of hay of similar shape, the diameters of their bases being respectively 10, 12, and 14 feet; if the smallest stack contains 2 tons, what will each of the others contain?

745. General Review, No. 6.

58. Supply the 2d term in the proportion 3 : x = 8:25. 59. What is the mean proportional between 0.8 and 0.72 ? 60. Divide $1900 between two men, in the proportion of 3 to 5. 61. Divide $ 45 among three boys, so that one shall have as much as the other two, whose shares are as 2 to 7.

62. How many pounds can 5 horses draw, if 6 horses can draw as much as 10 oxen, and 2 oxen can draw 2400 pounds? 63. Smith and Lee formed a partnership. Smith put in $1000 for 6 months and $800 for 2 months. Lee put in $600 for 8 months and was allowed $800 for his services. They gained $1435.50; what was each partner's share?

64. What is the 5th power of 23? the cube of 96 ?

65. What is the largest number of men in a regiment of 1000 that can be arranged in a square; and how many men will remain? How many men will there be on each side of the square?

66. How many feet of fencing are required to enclose a square farm containing 15 acres?

67. A ladder 27 feet long reaches a window 25% feet from the ground. How far does the foot of the ladder stand from the house?

68. What is the diameter of a circle which contains 314 square feet?

69. How many rods of fencing on both sides of a road which surrounds a circular park containing 15.708 acres, the road being 3 rods wide?

70. What must be the depth of a pail that is 10 inches across, to contain 5 gallons, the sides being upright?

71. How many square feet of canvas are required to construct a conical tent 14 feet across the bottom and 93 feet from the highest point to the ground?

72. If a pipe 2 inches in diameter will fill a cistern in two hours, in what time will a pipe 5 inches in diameter fill the same?

746. Questions for Review.

What is a power? a second power? a third? a fourth? What is INVOLUTION? What is squaring a number? cubing a number? Give the squares of the numbers from 1 to 12; the cubes of the numbers from 1 to 10.

What is the root of a number? What is EVOLUTION? Repeat the formula used in extracting the square root; the rule. What do you do when a term of the root proves too large? when the trial divisor is not contained in the dividend? How do you extract the square root of a fraction? of a mixed number? Repeat the formula used in extracting the cube root; the rule. How do you extract the cube root of a fraction? of a mixed number?

What is MENSURATION? Name and describe the different kinds of triangles given; the different kinds of quadrilaterals given. What is the base of a triangle? the height?

How do you find the area of a square? of a rectangle? of any parallelogram? of a triangle? of a trapezoid? of any polygon? How do you find the circumference of a circle when the diameter is given? when the radius is given? How do you find the diameter when the circumference is given? How do you find the area of a circle when the radius is given? the radius of a circle when the area is given?

What is a cube? a prism? a pyramid? a cylinder? a cone? What is the frustum of a pyramid or a cone? What is a sphere? Draw or name something in the form of each of these solids. What is the height of any solid? the slant height of a pyramid or of a cone? the slant height of a frustum of a pyramid or of a cone?

How do you find the volume of a cube? of any rectangular solid ? of a prism or a cylinder? of a pyramid or a cone? of the frustum of a pyramid or cone? How do you find the convex surface of each of these solids?

When the diameter and height are given, how do you find the volume of a cylinder? of a cone? of a frustum of a cone? How do you find the volume of a sphere? How do you find the convex surface of a cylinder? of a cone? of the frustum of a cone? of a sphere ?

When are plane figures similar? What proportion is there between the areas of similar figures? When are solids similar? What proportion is there between the volumes of similar solids?

747. Miscellaneous Examples.

73. What is the weight of a bale of cloth containing 13 pieces, 42 yards to the piece, every 3 yards weighing 14 pounds?

74. The sum of three numbers is 55; two of them are 144 and 2411; what is the third?

75. § + 3 + } + † of a certain number increased by 31 equals 40. What is the number?

76. A trader bought apples at $ 1.62 per barrel, and immediately sold them at $2.25, making $234.37. How many

barrels were bought?

77. Suppose a dividend to be 241.3, and the quotient 0.127, what was the divisor?

78. The ridge-pole of a house is 46 feet from the ground, the eaves 38 feet, the rafters on each side of the roof to the eaves being 18 feet long. What is the width of the house?

79. When the ice upon a pond is 10 inches thick, what will be the value of the ice taken from one acre of the pond at of a cent a pound, 1 cubic foot of ice containing 58 pounds?

80. The city tax of Lincoln being %, and the State and county tax 0.15%; for what sum is James Otis taxed, who pays $56.22, including $1.50 poll-tax?

81. Of what number is the part?

82. A city collector received 0.8 % for collecting taxes; he paid into the treasury $94625.64 after deducting his commission; what was the whole sum collected?

83. A coal-dealer purchased 500 tons of coal at $7.50 per long ton, paid $1 per ton for freighting, and sold it for $11 by the short ton. What per cent did he gain?

84. A can do a piece of work in 13 hours, A and B in 48 min.; in what time can B do it alone?

85. Crane Brothers & Co. purchased oil stocks to the amount of $5715.00, including their commission of %; the stock, the par value of which was $50 per share, was purchased at 95%. How many shares were purchased?

86. When butter is 25 cents a pound, and 3 of a pound will pay for of a dozen eggs, how many eggs will be required to pay for 6 pounds of raisins, 7 pounds of which cost 98 cents? 87. What is the difference between the true and bank discount of $700, due in 90 days, when the legal rate is 7% ?

88. How much would you receive from a bank, June 12, 1878, for a note of $820, dated April 12, 1878, payable 6 months after date, discount being 6% ?

89. Write a note for 60 days, for which you should get $300 at a bank, discount being 6% ?

90. If $1239 were paid for harvesting the wheat on a lot of land 400 rods long, 350 rods wide, what should be paid for harvesting the oats upon a lot 500 rods long, 450 rods wide, the cost of harvesting oats being as much as for harvesting wheat? 91. Bates and Henricks traded in hides for one year. Bates put in $2000 at first; at the end of 3 months he withdrew $700, and at the end of 7 months put in $1000. Henricks put in $1200 at first, and $500 more in 4 months. At the end of 6 months he withdrew $200. The gain for the year was $2355.75, of which Henricks received $1000 for conducting the business. What was the share of each ?

92. The pyramid of Cheops, in Egypt, is said to contain 82111000 cubic feet of masonry, and to have been 480 feet high. Allowing 7000000 cubic feet, which are required to perfect its pyramidal form and to fill its chambers, what is the length of one side of its base, which is a square?

93. If you buy figs at the rate of 9 pounds for $1.50, and sell them at the rate of 10 pounds for $2, what per cent do you gain?

94. What is the average time for paying for $200 worth of goods purchased May 17, 1877, on 4 months' credit; $500 worth, purchased June 18, 1877, on 60 days' credit; and $300 worth, purchased June 19, 1877, on 90 days' credit?

95. The captain of a ship at sea finds by his chronometer, at 12 o'clock, noon, that it is 45 m. past 8 o'clock in the evening at London. What is his longitude?